1. Field of the Invention
The present invention relates to a field of superconducting electronics, and particularly relates to a superconducting sigma-delta modulator.
2. Description of the Related Art
FIG. 6 is a circuit diagram showing a superconducting single-loop sigma-delta modulator described, for example, in the following Non-Patent Document 1. The sigma-delta modulator is a modulator which utilizes an integrating function (sigma) and a differentiating function (delta).
A superconducting inductor 602 is connected between nodes 604 and 605. An input voltage source 601 is connected between the node 604 and a ground. A Josephson junction 603 is connected between the node 605 and the ground. When a sampling clock signal SMP is supplied to the node 605, an output signal Y(z) is output from the node 605.
The input voltage source 601 supplies an input signal to the node 604. The superconducting inductor 602 composes an integrator, and a current obtained by integrating the input signal flows through the superconducting inductor 602. The Josephson junction 603 composes a quantizer and has a property of outputting a voltage pulse corresponding to a digital value “1” when the current flowing through the Josephson junction 603 is larger than a threshold and outputting no voltage pulse corresponding to the digital value “0” when the current is smaller than the threshold. A single flux quantum Φ0 is obtained by time-integrating this voltage pulse. The single flux quantum Φ0 is 2.07 fWb and corresponds to a voltage pulse of 2.07 mV·ps. When the Josephson junction 603 outputs the single flux quantum Φ0, the integrated current flowing through the superconducting inductor 602 is reduced by an amount corresponding to a single flux quantum (Φ0/L). Here, L is an inductance of the superconducting inductor 602. By performing such single-loop feedback, the sigma-delta modulated signal Y(z) is output. The Josephson junction 603 performs analog to digital (A/D) conversion by quantization in response to the sampling clock signal SMP. The output signal Y(z) becomes a time series of the digital value “1” and “0”. By using this sigma-delta modulator, an A/D converter can be constructed.
FIG. 7 shows another superconducting single-loop sigma-delta modulator described, for example, in the following Non-Patent Document 2.
An input current source 701 is connected in series to a superconducting inductor 702. The superconducting inductor 702 is magnetically coupled to a superconducting inductor 704. A Josephson junction 703 is connected between a node 712 and the ground. The superconducting inductor 704 is connected between nodes 712 and 711. A Josephson junction 705 is connected between the node 711 and the ground. An input terminal of a single flux quantum inverter circuit 706 is connected to the node 711, and an output terminal thereof is connected to the node 712. The output signal Y(z) is output from the node 711. Incidentally, similarly to FIG. 6, the sampling clock signal SMP is supplied to the Josephson junction 705 and the single flux quantum inverter circuit 706.
An input signal of the input current source 701 is supplied to the superconducting inductor 704 via mutual inductance M between the superconducting inductors 702 and 704. The superconducting inductor 704 composes an integrator. The Josephson junctions 703 and 705 operate complementarily so as to realize bipolar feedback. For example, when the input signal is maintained at 0 and the Jopsephson junction 705 outputs “0” without outputting the single flux quantum Φ0, the single flux quantum inverter circuit 706 logically inverts an input signal of “0” and outputs the single flux quantum Φ0. Then, the Josephson junction 703 outputs the single flux quantum Φ0. When the Josephson junction 705 outputs the single flux quantum Φ0, the single flux quantum inverter circuit 706 logically inverts an input signal of the single flux quantum Φ0 and outputs “0”. Then, the Josephson junction 703 outputs “0”. As just described, the Josephson junctions 703 and 705 balance a mean voltage at both ends of the inductor 704 while maintaining a complementary relationship. Here, the mean voltage at both ends of the inductor 704 is equal to a mean voltage of the Josephson junctions 703 and 705 and given by V=f×Φ0 when the frequency at which the Josephson junctions switch is f[Hz].
As shown in FIG. 6, in the superconducting single-loop sigma-delta modulator, the modulator can be composed of only a set of the superconducting inductor 602 and the Josephson junction 603. In the superconducting sigma-delta modulator, the feedback is one flux quantum Φ0, and quantum mechanical feedback with a precision of a physical constant can be utilized, whereby high resolution can be expected. It is known that in the single-loop sigma-delta modulator, by first-order noise shaping, the SN ratio improves by 9 dB/octave with an increase of sampling frequency.
On the other hand, in a second-order sigma-delta modulator with second-order noise shaping, the SN ratio improves by 15 dB/octave with an increase of sampling frequency, so that there is an advantage of being able to obtain a high SN ratio without increasing the oversampling ratio considerably, but it has not been easy to realize the second-order sigma-delta modulator by a superconducting single flux quantum (SFQ) circuit. A superconducting second-order low-pass sigma-delta modulator known to date is a double-loop type having two feedback loops.
FIG. 8 is a circuit diagram of a superconducting double-loop sigma-delta modulator, for example, described in Non-Patent Document 3. An input signal X(z) is supplied to a node 801. A resistance R1 is connected between the node 801 and the ground. A series connection of a superconducting inductor L1 and a feedback driver 802 is connected between nodes 801 and 803. A resistance R2 is connected between the node 803 and the ground. A superconducting inductor L2 is connected between nodes 803 and 804. A Josephson junction 805 is connected between the node 804 and the ground. The sampling clock signal SMP is supplied to the node 804. The output signal Y(z) of the node 804 is fed back as a trigger signal of the feedback driver 802. The feedback driver 802 can output multiple number of flux quanta of M×Φ0. The output signal Y(z) triggers two feedback loops: feedback to an integrator of the superconducting inductor L2 and feedback to an integrator of the superconducting inductor L1.
Moreover, in the following Patent Document 1, a second-order sigma-delta modulator is described. However, a method of realizing the second-order sigma delta modulator using superconductivity is not described.
(Non-Patent Document 1)
IEEE Trans. Appl. Supercond., Vol. 3, pp. 2732–2735, March 1993.
(Non-Patent Document 2)
IEEE Trans. Appl. Supercond. Vol. 9, pp. 4026–4029, June 1999.
(Non-Patent Document 3)
IEEE Trans. Appl. Supercond. Vol. 5, pp. 2248–2251, June 1995.
(Non-Patent Document 4)
Technical Report of the Institute of Electronics, Information and Communication Engineers, SCE2003-27, Oct. 17, 2003
(Patent Document 1)
Japanese Patent Publication No. Hei 3-928
(Patent Document 2)
Japanese Patent Application Laid-open No. 2001-102929
The modulator in FIG. 8 needs the feedback driver 802 which feeds back multiple (the number M of) single flux quanta to the second feedback loop. This feedback driver 802 is very difficult to design using the technology of a single flux quantum circuit having small driving force by nature, which becomes a bottleneck in realizing a high-order low-pass sigma-delta modulator.
FIG. 9 is a graph showing a relation between an SN ratio of each type of low-pass sigma-delta modulator and a sampling frequency. The analog signal bandwidth is assumed to be 100 MHz. A curve 901 represents an SN ratio of the superconducting single-loop sigma-delta modulators shown in FIG. 6 and FIG. 7. The SN ratio of the superconducting single-loop sigma-delta modulator coincides with an SN ratio of a model of an ideal first-order sigma-delta modulator. A curve 902 shows an SN ratio calculated from an analytical solution of a transfer function of the superconducting double-loop sigma-delta modulator (M=64) in FIG. 8. A curve 903 shows a curve representing an SN ratio of a model of an ideal second-order sigma-delta modulator. The SN ratio of the superconducting double-loop sigma-delta modulator with the curve 902 does not coincide with the SN ratio of the model of the ideal second-order sigma-delta modulator with the curve 903, and hence it can be seen that although the SN ratio higher than the SN ratio of the superconducting single-loop sigma-delta modulator of the curve 901 can be obtained, the gain M of the feedback driver 802 is considerably high, and that the sufficient SN ratio cannot be achieved unless the sampling frequency is set sufficiently high. In the case of the feedback gain M=64 shown, a circuit scale of several hundred junctions is necessary in order to compose the modulator, whereby not only design but also circuit fabrication is difficult.